探索Jean Bourgain的工具包

IF 2 3区数学 Q1 MATHEMATICS

Bulletin of the American Mathematical Society Pub Date : 2020-09-14 DOI:10.1090/BULL/1716

T. Tao

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引用次数: 12

摘要

吉安-卡洛·罗塔曾断言:“每个数学家都只有一些技巧”。乍一看，让·布尔甘作品的广度和独创性似乎是这条格言的反例。然而，正如我们希望在本文中说明的那样，即使是布尔甘也经常依赖于一组核心工具，这些工具构成了许多不同数学领域的问题可以被攻击的基础。我们在这里讨论其中一些工具，然后进行一个案例研究，说明布尔甘的一篇论文中的论点如何被解释为这些工具中几个的连续应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Exploring the toolkit of Jean Bourgain

Gian-Carlo Rota once asserted that "every mathematician only has a few tricks". The sheer breadth and ingenuity in the work of Jean Bourgain may at first glance appear to be a counterexample to this maxim. However, as we hope to illustrate in this article, even Bourgain relied frequently on a core set of tools, which formed the base from which problems in many disparate mathematical fields could then be attacked. We discuss a selected number of these tools here, and then perform a case study of how an argument in one of Bourgain's papers can be interpreted as a sequential application of several of these tools.

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来源期刊

Bulletin of the American Mathematical Society 数学-数学

CiteScore

2.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.